#!/usr/bin/env python3
"""Print the canonical Rust heading table; integer arithmetic only.

Run: python3 scripts/generate-heading-table.py > crates/hexwork-core/src/heading_table.rs
Pi is a fixed, independently published decimal constant, not host libm output.
Taylor series in [0, pi/2], at 70 decimal fixed-point digits, then quadrant
reflection gives reproducible rounded 1e9 unit vectors on every Python host.
"""
SCALE = 10**70
PI = 314159265358979323846264338327950288419716939937510582097494459230781640628620899
# PI above is floor(pi * 10**80).
PI_FIXED = PI // 10**10
UNIT = 10**9


def nearest(n, d):
    return (n + d // 2) // d if n >= 0 else -((-n + d // 2) // d)


def sine(angle):
    term = angle
    total = term
    k = 1
    while term:
        term = -nearest(term * angle * angle, SCALE * SCALE * (2*k) * (2*k+1))
        total += term
        k += 1
    return nearest(total * UNIT, SCALE)


quarter = [sine(nearest(PI_FIXED * i, 2048)) for i in range(1025)]
assert quarter[0] == 0 and quarter[1024] == UNIT
assert quarter[512] == 707106781
vectors = []
for heading in range(4096):
    quadrant, offset = divmod(heading, 1024)
    s, c = quarter[offset], quarter[1024-offset]
    vectors.append(((s, -c), (c, s), (-s, c), (-c, -s))[quadrant])
print('// @generated by scripts/generate-heading-table.py; do not edit.')
print('pub(super) const UNIT_VECTORS: [[i64; 2]; 4096] = [')
for x, y in vectors:
    print(f'    [{x}, {y}],')
print('];')